Properties

Label 5445.2.a
Level $5445$
Weight $2$
Character orbit 5445.a
Rep. character $\chi_{5445}(1,\cdot)$
Character field $\Q$
Dimension $181$
Newform subspaces $56$
Sturm bound $1584$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 56 \)
Sturm bound: \(1584\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(23\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5445))\).

Total New Old
Modular forms 840 181 659
Cusp forms 745 181 564
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(+\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(24\)
\(-\)\(-\)\(-\)\(-\)\(30\)
Plus space\(+\)\(85\)
Minus space\(-\)\(96\)

Trace form

\( 181 q - q^{2} + 175 q^{4} - q^{5} - 4 q^{7} - 9 q^{8} + O(q^{10}) \) \( 181 q - q^{2} + 175 q^{4} - q^{5} - 4 q^{7} - 9 q^{8} - 3 q^{10} - 10 q^{13} - 24 q^{14} + 159 q^{16} + 6 q^{17} - 12 q^{19} - 7 q^{20} - 8 q^{23} + 181 q^{25} + 10 q^{26} + 12 q^{28} - 6 q^{29} + 4 q^{31} - 29 q^{32} + 6 q^{34} + 4 q^{35} - 2 q^{37} + 12 q^{38} - 3 q^{40} + 14 q^{41} - 16 q^{43} + 28 q^{46} - 28 q^{47} + 169 q^{49} - q^{50} + 10 q^{52} - 26 q^{53} - 4 q^{56} + 50 q^{58} - 16 q^{59} + 6 q^{61} + 32 q^{62} + 191 q^{64} + 2 q^{65} - 20 q^{67} + 66 q^{68} + 16 q^{70} + 12 q^{71} - 22 q^{73} - 14 q^{74} + 44 q^{76} - 32 q^{79} + q^{80} + 82 q^{82} - 14 q^{85} + 32 q^{86} - 42 q^{89} - 48 q^{91} - 4 q^{92} + 76 q^{94} + 12 q^{95} - 114 q^{97} + 55 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5445))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11
5445.2.a.a 5445.a 1.a $1$ $43.479$ \(\Q\) None \(-2\) \(0\) \(-1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.b 5445.a 1.a $1$ $43.479$ \(\Q\) None \(-2\) \(0\) \(1\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.c 5445.a 1.a $1$ $43.479$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{13}+\cdots\)
5445.2.a.d 5445.a 1.a $1$ $43.479$ \(\Q\) None \(-1\) \(0\) \(-1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots\)
5445.2.a.e 5445.a 1.a $1$ $43.479$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
5445.2.a.f 5445.a 1.a $1$ $43.479$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
5445.2.a.g 5445.a 1.a $1$ $43.479$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
5445.2.a.h 5445.a 1.a $1$ $43.479$ \(\Q\) None \(1\) \(0\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
5445.2.a.i 5445.a 1.a $1$ $43.479$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{13}+\cdots\)
5445.2.a.j 5445.a 1.a $1$ $43.479$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
5445.2.a.k 5445.a 1.a $1$ $43.479$ \(\Q\) None \(2\) \(0\) \(-1\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.l 5445.a 1.a $1$ $43.479$ \(\Q\) None \(2\) \(0\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.m 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
5445.2.a.n 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots\)
5445.2.a.o 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
5445.2.a.p 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.q 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-\beta q^{7}+4q^{16}-2\beta q^{17}+\cdots\)
5445.2.a.r 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
5445.2.a.s 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.t 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.u 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.v 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots\)
5445.2.a.w 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
5445.2.a.x 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots\)
5445.2.a.y 5445.a 1.a $2$ $43.479$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.z 5445.a 1.a $3$ $43.479$ 3.3.148.1 None \(-1\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ba 5445.a 1.a $3$ $43.479$ 3.3.469.1 None \(-1\) \(0\) \(-3\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bb 5445.a 1.a $3$ $43.479$ 3.3.404.1 None \(-1\) \(0\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bc 5445.a 1.a $3$ $43.479$ 3.3.469.1 None \(1\) \(0\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bd 5445.a 1.a $3$ $43.479$ 3.3.404.1 None \(1\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.be 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(-5\) \(0\) \(4\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1}+\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bf 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(-3\) \(0\) \(-4\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bg 5445.a 1.a $4$ $43.479$ 4.4.2525.1 None \(-3\) \(0\) \(-4\) \(11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
5445.2.a.bh 5445.a 1.a $4$ $43.479$ 4.4.48704.2 None \(-2\) \(0\) \(4\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bi 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(-1\) \(0\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bj 5445.a 1.a $4$ $43.479$ \(\Q(\zeta_{15})^+\) None \(-1\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bk 5445.a 1.a $4$ $43.479$ 4.4.5725.1 None \(-1\) \(0\) \(4\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5445.2.a.bl 5445.a 1.a $4$ $43.479$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{5}+2\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5445.2.a.bm 5445.a 1.a $4$ $43.479$ 4.4.27648.1 None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots\)
5445.2.a.bn 5445.a 1.a $4$ $43.479$ 4.4.27648.1 None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5445.2.a.bo 5445.a 1.a $4$ $43.479$ 4.4.8112.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots\)
5445.2.a.bp 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(1\) \(0\) \(4\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bq 5445.a 1.a $4$ $43.479$ \(\Q(\zeta_{15})^+\) None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5445.2.a.br 5445.a 1.a $4$ $43.479$ 4.4.5725.1 None \(1\) \(0\) \(4\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bs 5445.a 1.a $4$ $43.479$ 4.4.48704.2 None \(2\) \(0\) \(-4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bt 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(3\) \(0\) \(-4\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bu 5445.a 1.a $4$ $43.479$ 4.4.2525.1 None \(3\) \(0\) \(-4\) \(-11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bv 5445.a 1.a $4$ $43.479$ 4.4.725.1 None \(5\) \(0\) \(4\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bw 5445.a 1.a $6$ $43.479$ 6.6.74043072.1 None \(0\) \(0\) \(-6\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
5445.2.a.bx 5445.a 1.a $6$ $43.479$ 6.6.27433728.1 None \(0\) \(0\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots\)
5445.2.a.by 5445.a 1.a $6$ $43.479$ 6.6.74043072.1 None \(0\) \(0\) \(6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
5445.2.a.bz 5445.a 1.a $6$ $43.479$ 6.6.437199552.1 None \(0\) \(0\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ca 5445.a 1.a $8$ $43.479$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(-8\) \(8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cb 5445.a 1.a $8$ $43.479$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(8\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cc 5445.a 1.a $8$ $43.479$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(-8\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
5445.2.a.cd 5445.a 1.a $8$ $43.479$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(8\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)